Polymers, methods of use thereof, and methods of decomposition thereof

ABSTRACT

Polymers, methods of use thereof, and methods of decomposition thereof, are provided. One exemplary polymer, among others, includes, a photodefinable polymer having a sacrificial polymer and a photoinitiator.

CROSS-REFERENCE TO RELATED APPLICATIONS

This is a Continuation Application that claims priority to applicationSer. No. 12/140,539, filed Jun. 17, 2008, which is a ContinuationApplication that claims priority to application Ser. No. 11/451,144,filed Jun. 12, 2006, which claims priority to co-pending U.S.application entitled “Polymers, Methods of Use There, and Methods ofDecomposition Thereof” having application Ser. No. 10/686,697, filedOct. 16, 2003, which claims priority to U.S. provisional applicationentitled “Fabrication of Microchannels using PolynorbornenePhotosensitive Sacrificial Materials” having Ser. No. 60/418,930, filedon Oct. 16, 2002, which is entirely incorporated herein by reference.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

The U.S. Government has a paid-up license in this invention and theright in limited circumstances to require the patent owner to licenseothers on reasonable terms as provided for by the terms of MDA awardedby the National Science Foundation (Grant #DMI-9980804) of the U.S.Government.

TECHNICAL FIELD

The present invention is generally related polymers, and, moreparticularly, is related to photodefinable polymers, methods of usethereof, and methods of decomposition thereof.

BACKGROUND

Microfluidic devices have tremendous potential for applications in avariety of fields including drug discovery, biomedical testing, andchemical synthesis and analysis. In such devices, liquids and gases aremanipulated in microchannels with cross-sectional dimensions on theorder of tens to hundreds of micrometers. Processing in suchmicrochannel devices offers a number of advantages including low reagentand analyte consumption, highly compact and portable systems, fastprocessing times, and the potential for disposable systems. However, inspite of all of their promise, microfluidic devices are currently beingused in a limited number of applications and are in general still rathersimple devices in terms of their operational complexity andcapabilities. For example, in terms of making truly portablemicroanalytical systems, one of the current difficulties involves thesimple integration of electronic (e.g., sensing methods) and fluidicelements into the same device. One of the most important issues, whichcontrols this ability to integrate functions into the same device, andthus controls the level of functionality of a microfluidic device is,the method used to fabricate the structure. In addition, fluidmicrodynamics through the microchannels is important to avoid mixing insystems where mixing is not needed.

The two most prevalent methods for fabricating microfluidic devices todate involve either bonding together layers of ultraflat glass orelastomeric polymers such as poly(dimethylsiloxane). Both methods sufferfrom severe limitations and difficulties associated with integratingnon-fluidic elements such as detectors with the microchannel system inthe same substrate. Other methods suffer from several limitationsincluding the fact that they require on the order of ten processingsteps to complete the sequence for a single level of microchannels.

SUMMARY OF THE INVENTION

Briefly described, embodiments of this disclosure, among others, includepolymers, methods of use thereof, and methods of decomposition thereof.One exemplary polymer, among others, includes a photodefinable polymerhaving a sacrificial polymer and a photoinitiator.

Methods of for fabricating a structure are also provided. One exemplarymethod includes, among others: disposing a photodefinable polymer onto asurface, wherein the photodefinable polymer includes a sacrificialpolymer and a photoinitiator selected from a negative tonephotoinitiator and a positive tone photoinitiator; disposing a grayscale photomask onto the photodefinable polymer, wherein the gray scalephotomask encodes an optical density profile defining athree-dimensional structure to be formed from the photodefinablepolymer, exposing the photodefinable polymer through the gray scalephotomask to optical energy; and removing portions of the photodefinablepolymer to form the three-dimensional structure of cross-linkedphotodefinable polymer.

In addition, methods of decomposing a polymer are also provided. Oneexemplary method includes, among others: providing a structure having asubstrate, an overcoat layer, and a polymer in a defined area within theovercoat layer; maintaining a constant rate of decomposition as afunction of time; and removing the polymer from the area to form anair-region in the defined area.

Furthermore, a structure is provided. One exemplary structure includes asubstrate; an air-region area having a spatially-varying height; and anovercoat layer disposed onto a portion of the substrate and engaging asubstantial portion of the air-region area.

Other systems, methods, features, and advantages will be, or become,apparent to one with skill in the art upon examination of the followingdrawings and detailed description. It is intended that all suchadditional systems, methods, features, and advantages be included withinthis description, be within the scope of the present invention, and beprotected by the accompanying claims.

BRIEF DESCRIPTION OF THE DRAWINGS

Many aspects of this disclosure can be better understood with referenceto the following drawings. The components in the drawings are notnecessarily to scale, emphasis instead being placed upon clearlyillustrating the principles of this disclosure. Moreover, in thedrawings, like reference numerals designate corresponding partsthroughout the several views.

FIG. 1 illustrates representative embodiments of photoinitiators.

FIG. 2 illustrates a cross-sectional view of a representative structurehaving an embodiment on an air-region.

FIGS. 3A through 3F are cross-sectional views that illustrate arepresentative method of fabricating the structure illustrated in FIG.2.

FIGS. 4A through 4D illustrate the cross sections of the four simulatedchannels. FIG. 4A illustrates the dimensions of a uniform area channel.FIGS. 4B and 4C illustrate channels with tapered corners.

FIGS. 5A through 5C illustrate plots of the transit times for fluidpackets as a function of radial distance along the corner for a standardrectangular channel geometry turn, a triangular cross section channelturn, and an improved channel turn in a structure, respectively.

FIG. 6 illustrates curves of the decomposition rate versus time for purepolynorbornene (PNB) samples decomposed at both a constant temperatureof 425° C. (isothermal decomposition) and various heating rates (dynamicdecomposition), respectively.

FIG. 7 illustrates the temperature versus time heating profiles requiredto achieve decomposition rates of 1, 2, and 3% per minute using equation(6) in Example 1.

FIG. 8 illustrates the temperature versus time curve calculated usingequation (6) and the corresponding simple mimic heating profile that wastested in the Lindberg decomposition furnaces for device fabrication.

FIG. 9 illustrates thermogravimetric analysis (TGA) results for thesimple mimic heating program that was designed to achieve a 1% perminute decomposition rate.

FIGS. 10A through 10G illustrate scanning electron microscope (SEM)images of the channel encapsulated with polyimide and decomposed atdifferent rates using different heating profiles.

FIGS. 11A through 11F illustrate SEM images of channels encapsulatedwith SiO₂.

FIG. 12 illustrates the contrast curves for two photosensitive polymerformulations used in Example 1.

FIGS. 13 and 14 illustrate the real Feature I type PNB patterns producedas measured by profilometry, and for comparison the predictedmicrochannel patterns (using equations 7 through 10 in Example 1), forthe systems with 2 wt % and 4 wt % initiator loadings.

FIGS. 15A through 15D illustrates SEM images of the taperedmicrochannels.

FIG. 16 illustrates the predicted transit times for flow around amicrochannel corner using the boundary conditions and velocities used inthe earlier idealized channel simulations.

DETAILED DESCRIPTION

In general, polymer, methods of use thereof, structures formedtherefrom, and methods of decomposition thereof, are disclosed.Embodiments of the polymer can be used to form photodefinablethree-dimensional structures having unique spatial dimensions (e.g.,spatially-varying height) using photolithographic techniques. Inaddition, methods of decomposition can be used to decompose the polymerthree-dimensional structure located within a material (e.g., an overcoatlayer) without altering (e.g., deforming) the spatial boundaries definedby the photodefinable polymer three-dimensional structure.

Embodiments of the polymer include a photodefinable polymer. Thephotodefineable polymer includes, but is not limited to, one or moresacrificial polymers and one or more photoinitiators. The photoinitiatorcan include a negative tone photoinitiator and/or a positive tonephotoinitiator.

In general, negative tone photoinitiators can be used making thesacrificial polymer more difficult to remove (e.g., more stable towardsa solvent that normally would dissolve the sacrificial polymer). Forexample, half of a layer of a photodefinable polymer (including asacrificial polymer and a negative tone photoinitiator) is exposed tooptical energy (e.g., ultraviolet (UV) light, near-ultraviolet light,and/or visible light), while the other half is not exposed.Subsequently, the entire layer is exposed to a solvent and the solventdissolves the layer not exposed to the UV light.

More specifically, the area exposed includes a cross-linkedphotodefinable polymer, while portions not exposed include anuncross-linked photodefinable polymer. The uncross-linked photodefinablepolymer can be removed with the solvent leaving the cross-linkedphotodefinable polymer (e.g., the photodefinable three-dimensionalstructure).

Although not intending to be bound by theory, upon exposure to opticalenergy, one type, among others, of the negative tone photoinitiator cangenerate free radicals that initiate cross-linking reactions between thesacrificial polymers to form a cross-linked photodefinable polymer. As aresult, gray scale lithography can be used to fabricate photodefinablethree-dimensional structures from the photodefinable polymer by removingthe uncross-linked photodefinable polymer.

In general, positive tone photo initiators can be used making thesacrificial polymer easier to remove (e.g., less stable towards asolvent). For example, half of a layer of a photodefinable polymer(including a sacrificial polymer and a positive tone photoinitiator) isexposed to UV light, while the other half is not exposed. Subsequently,the entire layer is exposed to a solvent and the solvent dissolves thelayer exposed to the UV light.

Although not intending to be bound by theory, upon exposure to opticalenergy, the positive tone photoinitiator generates an acid. Then, uponexposure to a base, the dissolution of the sacrificial polymer isincreased relative to sacrificial polymer not exposed to optical energy.As a result, gray scale lithography can be used to fabricatephotodefinable three-dimensional structures from the photodefinablepolymer by removing the exposed photodefinable polymer.

In general, the photodefinable polymer can be used in areas such as, butnot limited to, microelectronics (e.g., microprocessor chips,communication chips, and optoeletronic chips), microfluidics, sensors,analytical devices (e.g., microchromatography), as a sacrificialmaterial to create photodefinable three-dimensional structures that canbe subsequently formed into photodefinable air-regions by thermallydecomposing the photodefinable polymer. In addition, the photodefinablepolymer can be used as an insulator, for example.

For embodiments using the photodefinable polymer as a sacrificialmaterial to create photodefinable air-regions having photodefinablethree-dimensional structures, the decomposition of the photodefinablepolymer should produce gas molecules small enough to permeate one ormore of the materials surrounding the photodefinable polymer (e.g., anovercoat polymer layer). In addition, the photodefinable polymer shouldslowly decompose so as to not create undue pressure build-up whileforming the air-region within the surrounding materials. Furthermore,the photodefinable polymer should have a decomposition temperature lessthan the decomposition or degradation temperature of the surroundingmaterial. Still further, the photodefinable polymer should have adecomposition temperature above the deposition or curing temperature ofan overcoat material but less than the degradation temperature of thecomponents in the structure in which the photodefinable polymer is beingused.

The sacrificial polymer can include compounds such as, but not limitedto, polynorbornenes, polycarbonates, polyethers, polyesters,functionalized compounds of each, and combinations thereof. Thepolynorbornene can include, but is not limited to, alkenyl-substitutednorbornene (e.g., cyclo-acrylate norbornene). The polycarbonate caninclude, but is not limited to, norbornene carbonate, polypropylenecarbonate, polyethylene carbonate, polycyclohexene carbonate, andcombinations thereof. In addition, the molecular weight of thesacrificial polymer should be between 10,000 and 200,000.

The sacrificial polymer can be from about 1% to 30% by weight of thephotodefinable polymer. In particular, the sacrificial polymer can befrom about 5% to 15% by weight of the photodefinable polymer.

As mentioned above, the photoinitiator can include negative tonephotoinitiators and positive tone photoinitiators. The negative tonephotoinitiator can include compounds that generate a reactant that wouldcause the crosslinking of the sacrificial polymer. The negative tonephotoinitiators can include compounds, such as, but not limited to, aphotosensitive free radical generator. Alternative negative tonephotoinitiators can be used such as photoacid generators (e.g., in anepoxide functionalized systems).

A negative tone photosensitive free radical generator is a compoundwhich, when exposed to light breaks into two or more compounds, at leastone of which is a free radical. In particular, the negative tonephotoinitiator can include, but is not limited to,bis(2,4,6-trimethylbenzoyl)-phenylphosphineoxide (Structure 1 in FIG. 1)(Irgacure 819, Ciba Specialty Chemicals Inc.),2-benzyl-2-dimethylamino-1-(4-morpholinophenyl)-butanone-1 (Structure 2in FIG. 1) (Irgacure 369, Ciba), 2,2-dimethoxy-1,2-diphenylethan-1-one(Structure 3 in FIG. 1) (Irgacure 651, Ciba),2-methyl-1[4-(methylthio)-phenyl]-2-morpholinopropan-1-one (Structure 4in FIG. 1) (Irgacure 907, Ciba), benzoin ethyl ether (Structure 5 inFIG. 1) (BEE, Aldrich),2-methyl-4′-(methylthio)-2-morpholino-propiophenone,2,2′-dimethoxy-2-phenyl-acetophenone (Irgacure 1300, Ciba), andcombinations thereof. In particular, the photoinitiator can includebis(2,4,6-trimethylbenzoyl)-phenylphosphineoxide and2-benzyl-2-dimethylamino-1-(4-morpholinophenyl)-butanone-1.

The positive tone photoinitiators can include, but are not limited to,photoacid generators. More specifically, the positive tonephotoinitiator can include, but is not limited to, nucleophilichalogenides (e.g., diphenyliodonium) and complex metal halide anions(e.g., triphenylsulphonium salts).

The photoinitiator can be from about 0.5% to 5% by weight of thephotodefinable polymer. In particular, the photoinitiator can be fromabout 1% to 3% by weight of the photodefinable polymer.

The remaining percentage of the photodefinable polymer not accounted forin the photoinitiator and sacrificial polymer (e.g., from 65% about to99%) to can be made up with solvent, such as, but not limited to,mesitylene MS, N-methyl-2-pyrrolidinone, propyleneglycol monomethylether acetate, N-butyl acetate diglyme, ethyl 3-ethoxypropionate, andcombinations thereof.

Exemplary photodefinable polymers include those shown in Table 1.

TABLE 2 Conditions and results for UV exposure response, with differentphotoinitiators and the loading of Irgacure 819 Recipe of PNB/PI Photo-Solution sensitivity Experiment# Photoinitiator PNB1/PI/MS (wt %)(mJ/cm²) Contrast 1 BEE 16/0.64/83.36 1959 0.908 2 Irgacure 90716/0.64/83.36 3641 0.651 3 Irgacure 651 16/0.64/83.36 1054 0.907 4Irgacure 369 16/0.64/83.36 1808 0.521 5 Irgacure 819 16/0.64/83.36 1341.213 6 Irgacure 819 16/0.32/83.68 363 0.879 7 Irgacure 81916/0.16/83.84 3236 0.448 Processing conditions: Spin-coating/2400 rpm,Softbake/110° C., 1 min, PEB/120° C., 30 min, Developer/xylene.

Now having described the photodefinable polymer in general, thefollowing describes exemplar embodiments for using the photodefinablepolymer to produce photodefinable three-dimensional structures, wherethe photodefinable three-dimensional structures can be decomposed toform photodefinable air-regions (e.g., a gas filled region substantiallyexcluding a solid or liquid material or a vacuum-region).

In general, a photodefinable three-dimensional structure can be producedby disposing a layer of the photodefinable polymer onto a substrateand/or layer of material on the substrate. A gray scale photomask isdisposed onto the photodefinable polymer or portions thereof thatencodes the photodefinable three-dimensional structure, as describedbelow. After exposing the photodefinable polymer through the gray scalephotomask to optical energy and removing the unexposed photodefinablepolymer (negative tone) or the exposed photodefinable polymer (positivetone), the photodefinable three-dimensional structure is formed.

The gray scale photomask encodes an optical density profile that definesthe three-dimensional photodefinable structure. Upon exposure of thegray scale photomask to optical energy, a known amount of optical energyis allowed to pass through portions of the gray scale photomask. Thedesign of the gray scale photomask is used to control the amount ofoptical energy allowed to pass through the gray scale photomask. Inparticular, the gray scale photomask can be designed to control theamount of optical energy allowed to pass through the gray scalephotomask as a function of the position on the gray scale photomask.Thus, the gray scale photomask can be designed and used to produce thethree-dimensional structure from the photodefinable polymer by alteringthe amount of optical energy allowed to pass through the gray scalephotomask as a function of the position on the gray scale photomask. Thegray scale photomask can be formed by method known in the art (U.S. Pat.No. 4,622,114).

The three-dimensional structures (and the corresponding photodefinableair-regions) can have cross-sectional areas section such as, but notlimited to, non-rectangular cross-sections, asymmetrical cross-sections,curved cross sections, arcuate cross sections, tapered cross sections,cross sections corresponding to an ellipse or segment thereof, crosssections corresponding to a parabola or segment thereof, cross sectionscorresponding to a hyperbola or segment thereof, and combinationsthereof. For example, the three-dimensional structures can include, butare not limited to, non-rectangular structures, non-square structures,curved structures, tapered structures, structures corresponding to anellipse or segment thereof, structures corresponding to a parabola orsegment thereof, structures corresponding to a hyperbola or segmentthereof, and combinations thereof. In addition, the three-dimensionalstructures can have cross-sectional areas having a spatially-varyingheight.

FIG. 2 is a cross-sectional view of a representative non-rectangular,tapered, and asymmetrical photodefinable air-region 12 having aphotodefinable three-dimensional structure. For example, thenon-rectangular, tapered, and asymmetrical photodefinable air-region 12can be used as a corner section in a microfluidic system. This use, aswell as others, is described in more detail in Example 1.

As shown in FIG. 2, the non-rectangular, tapered, and asymmetricalphotodefinable air-region 12 is positioned on a substrate 10. Anovercoat polymer layer 14 is disposed around the non-rectangular,tapered, and asymmetrical photodefinable air-region 12. In anotherembodiment, among others, the non-rectangular, tapered, and asymmetricalphotodefinable air-region 12 can be positioned above the substrate 10 inthe overcoat layer 14. In still another embodiment, among others, themultiple non-rectangular, tapered, and asymmetrical photodefinableair-regions and other air-regions can be positioned at multiple heights(e.g., stacked on top of one another or stacked in an offset manner) inthe overcoat layer 14.

Although not illustrated, the non-rectangular, tapered, and asymmetricalphotodefinable air-region 12 can be formed in conjunction with otherair-regions and/or air-channels to form microfluidic devices, sensors,and analytical devices, for example.

The substrate 10 can be used in systems such as, but not limited to,microprocessor chips, microfluidic devices, sensors, analytical devices,and combinations thereof. Thus, the substrate 10 can be made ofmaterials appropriate for the system. However, exemplar materialsinclude, but are not limited to, glasses, silicon, silicon compounds,germanium, germanium compounds, gallium, gallium compounds, indium,indium compounds, or other semiconductor materials and/or compounds. Inaddition, the substrate 10 can include non-semiconductor substratematerials, including any dielectric material, metals (e.g., copper andaluminum), or ceramics or organic materials found in printed wiringboards, for example.

The overcoat polymer layer 14 can be a modular polymer that includes thecharacteristic of being permeable or semi-permeable to the decompositiongases produced by the decomposition of a sacrificial polymer whileforming the non-rectangular, tapered, and asymmetrical photodefinableair-region 12. In addition, the overcoat polymer layer 14 has elasticproperties so as to not rupture or collapse under fabrication and useconditions. Further, the overcoat polymer layer 14 is stable in thetemperature range in which the photodefinable polymer decomposes.

Examples of the overcoat polymer layer 14 include compounds such as, forexample, polyimides, polynorbornenes, epoxides, polyarylenes ethers,parylenes, inorganic glasses, and combinations thereof. Morespecifically the overcoat polymer layer 14 includes compounds such asAmoco Ultradel™ 7501, BF Goodrich Avatrel™ Dielectric Polymer, DuPont2611, DuPont 2734, DuPont 2771, DuPont 2555, silicon dioxide, siliconnitride, and aluminum oxide. The overcoat polymer layer 14 can bedeposited onto the substrate 10 using techniques such as, for example,spin coating, doctor-blading, sputtering, lamination, screen orstencil-printing, chemical vapor deposition (CVD), and plasma-baseddeposition systems.

The non-rectangular, tapered, and asymmetrical photodefinable air-region12 is formed by the removal (e.g., decomposition) of a crosslinkedphotodefinable polymer (a negative tone photoinitiator) from a definednon-rectangular, tapered, and asymmetrical area as illustrated in FIG.2.

It should be noted that additional components could be disposed onand/or within the substrate, the overcoat layer, and/or thenon-rectangular, tapered, and asymmetrical photodefinable air-region 12.In addition, the additional components can be included in any structurehaving air-regions as described herein. The additional components caninclude, but are not limited to, electronic elements (e.g., switches andsensors), mechanical elements (e.g., gears and motors),electromechanical elements (e.g., movable beams and mirrors), opticalelements (e.g., lens, gratings, and mirror), opto-electronic elements,fluidic elements (e.g., chromatograph and channels that can supply acoolant), and combinations thereof.

Although the spatial boundaries of the non-rectangular, tapered, andasymmetrical photodefinable air-region 12 are not easily defined becauseof the varying lengths, heights, and widths of the air-region, thefollowing spatial boundaries are provided as exemplary lengths, heights,and widths. The non-rectangular, tapered, and asymmetricalphotodefinable air-region 12 height can range from about 0.01 to about100 micrometers. The non-rectangular, tapered, and asymmetricalphotodefinable air-region 12 width can be from about 0.01 to about10,000 micrometers. The non-rectangular, tapered, and asymmetricalphotodefinable air-region 12 length can range from 0.01 micrometersabout 100 meters. It should be noted that a plurality of air-regions canbe formed such that larger and/or more intricate (e.g., multiple curvesin the x-, y-, and z-planes) air-regions can be formed.

FIGS. 3A through 3F are cross-sectional views that illustrate arepresentative process for fabricating the non-rectangular, tapered, andasymmetrical photodefinable air-region 12 illustrated in FIG. 2. Itshould be noted that for clarity, some portions of the fabricationprocess are not included in FIGS. 3A through 3F. As such, the followingfabrication process is not intended to be an exhaustive list thatincludes all steps required for fabricating the non-rectangular,tapered, and asymmetrical photodefinable air-region 12. In addition, thefabrication process is flexible because the process steps may beperformed in a different order than the order illustrated in FIGS. 3Athrough 3F or some steps may be performed simultaneously.

FIG. 3A illustrates the substrate 10 having the photodefinable polymer16 (negative tone) disposed thereon. The photodefinable polymer 16 canbe deposited onto the substrate 10 using techniques such as, forexample, spin coating, doctor-blading, sputtering, lamination, screen orstencil-printing, melt dispensing, chemical vapor deposition (CVD), andplasma-based deposition systems.

FIG. 3B illustrates a gray scale photomask 18 disposed on thephotodefinable polymer 16. The gray scale photomask 18 encodes anoptical density profile that defines to the cross-section of thenon-rectangular, tapered, and asymmetrical photodefinable air-region 12.

FIG. 3C illustrates the uncross-linked photodefinable polymer region 16Aand the cross-linked photodefinable polymer region 16B after exposure ofthe gray scale photomask 18 to optical energy, while FIG. 3D illustratesthe removal of the uncross-linked photodefinable polymer region 16A. Theuncross-linked photodefinable polymer region 16A can be removed bydissolution in a liquid, such as a solvent, for example, or by anothermethod that can remove or dissolve the polymer.

FIG. 3E illustrates the formation of the overcoat layer 14 onto thecross-linked photodefinable polymer region 16B. The overcoat layer 14can be deposited onto the substrate using techniques such as, forexample, spin coating, doctor-blading, sputtering, lamination, screen orstencil-printing, melt dispensing, chemical vapor deposition (CVD), andplasma-based deposition systems.

FIG. 3F illustrates the decomposition of the cross-linked photodefinablepolymer region 16B to form the non-rectangular, tapered, andasymmetrical photodefinable air-region 12. The cross-linkedphotodefinable polymer region 16B can be decomposed by heating thecross-linked photodefinable polymer 16B to a temperature sufficient todecompose the polymer (e.g., about 425° C.).

The thermal decomposition the photodefinable polymer (cross-linkedphotodefinable polymer in FIGS. 3A through 3F) can alter the spatialboundaries or dimensions of the resultant air-region (non-rectangular,tapered, and asymmetrical photodefinable air-region 12 shown in FIG. 2)if the photodefinable polymer decomposes too fast. As discussed ingreater detail in Example 1, the thermal decomposition of thephotodefinable polymer can cause the air-region to bubble and/orcollapse (e.g., sag) in one or more areas of the air-region. Alterationof the spatial boundaries of the cross-section can cause problems forsystems where known and designed cross-sections are necessary for thesystem to function properly.

For example, fluidic systems often need to have a known flow profile toensure mixing is or is not occurring. If the channels in the fluidicsystem have regions with unknown cross-sections and/or cross-sectionsnot conforming to the design, the fluid flowing through the channel mayhave an unknown and an unpredictable flow profile.

Embodiments of this disclosure provide thermal decomposition profilesthat substantially eliminate alterations to the spatial boundaries ofthe air-region caused by the decomposition of the polymer (e.g.,sacrificial polymers and photodefinable polymers). Prior solutionsincluded using a constant temperature to decompose the polymer, whileothers used linear temperature profiles to decompose the polymer.Problems associated with both of these are described in more detail inExample 1.

Embodiments of this disclosure describe decomposing the polymer at aconstant rate of decomposition versus time. Thermal decompositionprofiles based on maintaining a constant decomposition rate as afunction of time can substantially eliminate alterations of the spatialboundaries of the air-region. In other words, the decomposition isperformed at a constant rate of mass loss (grams per minute) of thephotodefinable polymer.

Thermal decomposition profiles can be expressed by the thermaldecomposition profile expression (equation 6 in the following Example).

$T = {\frac{E_{a}}{R}\left\lbrack {\ln\frac{{A\left( {l - {rt}} \right)}^{n}}{r}} \right\rbrack}^{- 1}$where R is the universal gas constant, t is time, n is the overall orderof decomposition reaction, r the desired polymer decomposition rate, Ais the Arrhenius pre-exponential factor, and E_(a) is the activationenergy of the decomposition reaction. Thus, in order to design a thermaldecomposition profile it is helpful to specify four parameters: thethree kinetic parameters (A, E_(a) and n) that describe the polymerdecomposition for each polymer, and r the desired polymer decompositionrate. Example 1 describes the thermal decomposition profile expressionin greater detail.

It should be noted that not all thermal decomposition profiles producedecomposition of the polymer that do not alter the spatial boundaries ofthe air-region. Example 1 includes an illustrative polymer where thermaldecomposition profiles greater than about 2% decomposition/minute alterthe spatial boundaries of the air-region, while thermal decompositionprofiles below about 2% decomposition/minute do not alter the spatialboundaries of the air-region. Therefore, one skilled in the art couldeasily experimentally determine the appropriate thermal decompositionprofile through a sequence of experiments without undue experimentation.

One example, among others, for experimentally determining theappropriate thermal decomposition profile includes starting with a 5%decomposition/minute profile. If the spatial boundaries of theair-region are altered, then the thermal decomposition profile can bereduced to a 4% decomposition/minute profile or 2.5%decomposition/minute profile, for example. Alternatively, if the spatialboundaries of the air-region are not altered, then the thermaldecomposition profile can be increase by a 1% decomposition/minuteprofile or more, for example (i.e., form 5% decomposition/minute profileto 6% decomposition/minute profile). In any event, one skilled in theart can use the teachings of this disclosure to obtain an appropriatethermal decomposition profile for numerous desired configurations.

It should also be noted that the thermal decomposition profile coulddepend upon a variety of factors such as, for example, the materialssurrounding the photodefinable polymer, the hardness of the overcoat,and/or the glass transition temperature of the overcoat. Thus, thesevariables can be considered in the selection of the thermaldecomposition profile.

Example 1

The following is a non-limiting illustrative example of an embodiment ofthis disclosure that is described in more detail in Wu, et al., Journalof the Electrochemical Society, 150, 9, H205-H213 (2003), which isincorporated herein by reference. This example is not intended to limitthe scope of any embodiment of this disclosure, but rather is intendedto provide specific exemplary conditions and results. Therefore, oneskilled in the art would understand that many conditions can be modifiedto produce a desired result, and it is intended that these modificationsbe within the scope of the embodiments of this disclosure. In addition,additional details related to this example can be found in Wu, et al.,Journal of the Electrochemical Society, 149, 10, G555-G561 (2002) andWu, et al., J. Appl. Polym. Sci, 81, 5, 1186-1195 (2003), both of whichare incorporated herein by reference.

Example 1 describes the development of and demonstrates the use ofphotodefinable sacrificial polymer fabrication methods to producechannel geometries with non-rectangular, tapered, and asymmetricalshaped cross-sectional profiles. The ability to control the shape of thechannel cross-section is expected to be particularly useful in preciselycontrolling the flow of fluids in microchannel systems, for example. Theability to control fluid flow patterns and dispersion by controlling thechannel cross section is investigated herein through computational fluiddynamics simulations. It was found that non-rectangular, tapered, andasymmetrical shaped cross-sectional channel profiles are useful inpreserving “plug flow” conditions in curved microchannels, for example,and thus reducing dispersion of components in the flow. Therefore, thethermal decomposition of the photodefinable sacrificial polymers wasstudied in detail and novel heating protocols were developed thatmaintain the channel shape during decomposition. The use of thesemethods demonstrated using gray scale lithography to producemicrochannels with tapered cross sections.

Simulation of Flow in Curved Channels

When designing and fabricating microfluidic devices, it is almostinevitable that channels with curved shapes are needed. For example,when designing a long separation column on a chip, turning the channelinto a meandering path may be required to keep the device within somerequired size limits. In such cases, it can be extremely important toprecisely control the fluid flow pattern in the channel so as tominimize differences in the residence time distribution of fluidtraveling through the channel. In other words, one generally would liketo maintain near “plug flow” conditions in devices used for separations,analysis, and other fluidic operations to prevent mixing and loss ofspatial confinement of fluid samples after injection or separation. Oneparticular problem is minimizing residence time variations for fluidstraveling through corners and curved sections of microfluidic channels.In order to illustrate this point and investigate the improvements thatcould be realized by using channels with tapered cross sections, aseries of computational fluid dynamics simulations were performed.

FLUENT™, a computational fluid dynamics (CFD) simulation packageproduced by Fluent Inc., was used to simulate the flow in a series ofdifferent corner designs for microchannels. GAMBIT™, a preprocessoraccessory for FLUENT made by Fluent Inc., was used to construct thedesired model geometry, apply the meshing points to the model, anddefine the required boundary zones. Once defined, FLUENT was used tosimulate the flow pattern in each microchannel and to produce numericaland graphical results for each case.

A series of 90 degree turns in microchannels were simulated with varyingcross sectional geometries. FIGS. 4A through 4D illustrates the crosssections of the four simulated channels. FIG. 4A illustrates thedimensions of a uniform area channel. FIGS. 4B and 4C illustratechannels with tapered corners. The taper improved the flow aroundcorners with FIG. 4D representing a near optimized design. The insideradius of the turns was held constant at 60 μm and the outside radius ofthe turns was held constant at 120 μm. The same boundary conditions wereapplied in simulating the flow through these channels and a constantpressure outlet condition, which was assumed to be atmospheric pressure.In this case, water was used as the flow media, but the results shouldbe general to any Newtonian fluid under laminar flow conditions. Underthese conditions, the flow rates and Reynolds numbers are quite lowwhich indicates laminar flow conditions, and thus a laminar flow modelwas used in FLUENT for solution of these problems.

In order to look at the dispersion, which would occur in fluid flowingaround each of these microchannel corners, fluid packet trajectories andtransit times around each turn were calculated. FIGS. 5A through 5Cillustrate plots of the transit times for fluid packets as a function ofradial distance along the corner for a standard rectangular channelgeometry turn, a triangular cross section channel turn, and an improvedchannel turn in a structure, respectively. The appearance of differentlines of packet transit times on these plots are due to the fact thatfluid packets at different vertical positions within the channels alsoexperience slight dispersion due to low velocities near the top andbottom surfaces of the channel.

FIG. 5A illustrates that the standard rectangular channel geometry wouldresult in severe dispersion of an initially flat concentration profileafter traveling around the 90 degree turn. Under laminar flowconditions, the relatively uniform velocity profile across the channelcross section coupled with the longer path length for fluid at theoutside of the turn result in transit times which are a factor of 3 to 5larger for fluid at the outside radius as compared to fluid at theinside radius. This dispersion would be even more greatly exaggeratedfor the case of a 180 degree bend.

One natural solution to this problem is to decrease the velocity of thefluid near the inside radius of the turn in order to achieve equaltransit times for the fluid irrespective of radial position. One way toachieve this velocity modification is to alter the cross sectional areaof different regions of the channel.

FIG. 5B illustrates the transit time profile for fluid flowing around aturn in a triangular cross section channel. The reduced channel heightat the inside radius of the turn would be expected to slow the velocityof fluid along the inside of the turn. Indeed, FIG. 5B shows that thetriangular cross section overcompensates and results in longer transittimes for fluid near the inside radius as compared to fluid near theoutside radius. From close inspection of the FLUENT results, it is alsoapparent that channel sections that have two walls intersecting at acuteangles leads to significant dispersion in these regions, and thus acuteangles in the channel cross section geometry should be avoided ifpossible. Based on these facts, an optimization was performed to designan improved channel cross section profile that would result in minimaldispersion around the simulated turn.

FIG. 5C illustrates the fluid transit time results for such an improvedchannel structure. The transit time profile is essentially uniform forfluid flowing around a 90 degree corner using this improved shape. Thus,it is clear that by designing the cross-sectional shape of microchannelsin turns it should be possible to minimize dispersion in the flowprofiles.

Experimental

The sacrificial polymer used was Unity™ 4481P, which includes thecopolymer of 5-butyl norbornene (BuNB) and 5-alkenyl norbornene (ANB) inthe molar ratio 73/27, (Promerus LLC, Brecksville, Ohio). The polymerweight average molecular weight (M_(w)) and polydispersity index (PDI)were measured to be 425,000 and 3.74, respectively, by gel permeationchromatography using polystyrene calibration standards.Bis(2,4,6-trimethylbenzoyl)-phenylphosphineoxide (Irgacure 819, CibaSpecialty Chemicals Inc.) was used as a free radical photoinitiator(PI). Solutions of polynorbornene (PNB) and PI were prepared usingmesitylene (MS, 97%, Aldrich) as the solvent. Two differentformulations, PNB/PI/MS in a mole ratio of 16/0.32/84 (2 wt % initiatorrelative to dry polymer) and PNB/PI/MS in a mole ratio of 16/0.64/84 (4wt % initiator relative to dry polymer) (weight ratios), were used inthe experiments. After exposure and baking, polymer patterns weredeveloped using xylene (98.5+%, Aldrich).

Thermal decomposition characteristics of the sacrificial polymer wereinvestigated using a Seiko Instruments Inc. TG/DTA 320 system.Thermogravimetric analysis (TGA) measurements were performed under N₂ ata purge rate of 28 milliliters/minute (mil/min). The encapsulatedsacrificial polymer structures were thermally decomposed in a Lindbergtube furnace purged with N₂.

For microchannel fabrication, PNB/PI films were cast onto silicon wafersusing a Brewer Science CEE 100 spinner and hotplate system. About a 3.5to 4.0 micrometer (μm) thick PNB/PI film was obtained at a spin speed of2400 revolutions per minute (rpm) and a softbake of 110° C. for 60seconds (s). Film thicknesses were measured using a Veeco Dektakprofilometer. An OAI Mask Aligner equipped with an i-line filtered UVirradiation source (365 nanometers (nm) wavelength) was used to exposeand pattern the PNB/PI films. Before exposure, the intensity of UV lightsource was measured using an OAI Model 356 Exposure Analyzer with a 365nm probe. After exposure, samples were post-exposure baked at 120° C.for 30 minutes in an oven. Samples were developed using a continuousspray of xylene while the wafer was spun at 500 rpm.

Removal of any polymer residue from the developed patterns wasaccomplished using a PlasmaTherm reactive ion etching (RIE) system usingthe following conditions: 5 standard cubic centimeters per minute (sccm)of CHF₃, 45 sccm of O₂, 250 milliTorr (mTorr), 300 W, 35° C. The etchingrate of the polymer under these conditions is approximately 300 nm/min.Plasma enhanced chemical vapor deposition (PECVD) was performed todeposit a SiO₂ overcoat for encapsulation of the polymer channelpatterns. The SiO₂ was deposited with a PlasmaTherm PECVD using thefollowing conditions: 380 kHz RF frequency, 50 W power, 200° C., 550mTorr, and a gas mixture of N₂O (1400 sccm) and 2% SiH₄ diluted in N₂(400 sccm). The deposition rate for the oxide using these conditions isapproximately 50 nm/min.

Thermal Decomposition Program

For the thermal decomposition process, the fractional decomposition canbe calculated from the TG curve as shown in equation (1):

$\begin{matrix}{\alpha = \frac{W_{0} - W}{W_{0} - W_{f}}} & (1)\end{matrix}$where W₀ is the initial mass, W is the mass remaining at some timeduring the decomposition, and W_(f) is the final mass of the sample atthe end of the thermal cycle. The kinetic description for thermaldecomposition of the polymer is generally expressed as shown in equation(2):

$\begin{matrix}{\frac{\mathbb{d}\alpha}{\mathbb{d}t} = {{k\left( {1 - \alpha} \right)}^{n} = {A\;{\exp\left( {- \frac{E_{\alpha}}{RT}} \right)}\left( {1 - \alpha} \right)^{n}}}} & (2)\end{matrix}$where n is the overall order of decomposition reaction, A is theArrhenius pre-exponential factor, and E_(a) is the activation energy ofthe decomposition reaction.

In order to avoid a sudden and large release of the gaseousdecomposition products from the polymer patterns that may result indistortion of the channel structure, it is desired to keep thedecomposition rate

$\left( \frac{\mathbb{d}\alpha}{\mathbb{d}t} \right)$constant during the entire decomposition process. Assuming thedecomposition rate is equal to a constant, r, throughout thedecomposition process then:

$\begin{matrix}{{\frac{\mathbb{d}\alpha}{\mathbb{d}t} = r},{and},{t = 0},{\alpha = 0}} & (3)\end{matrix}$Integrating equation (3) gives the general desired result shown inequation (4):α=rt  (4)Assuming that the reaction order, activation energy, andpre-exponentional factor do not change significantly during thedecomposition,

$\frac{\mathbb{d}\alpha}{\mathbb{d}t}$and α can be replaced with r and rt respectively in equation (2) whichresults in the following equation:

$\begin{matrix}{r = {A\;{\exp\left( {- \frac{E_{\alpha}}{RT}} \right)}\left( {1 - {rt}} \right)^{n}}} & (5)\end{matrix}$It is now possible to rearrange equation (5) to solve for the necessarytemperature versus time profile that is required to maintain a constantrate of polymer decomposition throughout the entire process. Theexplicit expression for temperature versus time is shown in equation(6).

$\begin{matrix}{T = {\frac{E_{\alpha}}{R}\left\lbrack {\ln\frac{{A\left( {1 - {rt}} \right)}^{n}}{r}} \right\rbrack}^{- 1}} & (6)\end{matrix}$Thus, in order to design a heating profile it is necessary to specifyfour parameters: the three kinetic parameters (A, E_(a) and n) thatdescribe the polymer decomposition, and r the desired polymerdecomposition rate. Based on regression of TGA data performed inprevious experiments, the kinetic parameters for the polymer used herewere determined to be: A=5.8×10¹⁴ min⁻¹, E_(a)=207 kJ/mol and n=1.05.Thus, for a given constant decomposition rate, r, one can obtain a curveof temperature versus decomposition time.Results and Discussion

Decomposition Condition: Thermal decomposition of the photodefinablesacrificial polymer was performed in a pure nitrogen atmosphere in orderto avoid any oxidation of the polymer that could result in the formationof non-volatile decomposition products and undesirable residue in themicrochannels. In addition to using an inert atmosphere, as suggestedpreviously a controlled heating profile was used to maintain arelatively constant polymer decomposition rate. This constantdecomposition rate ensures that gaseous products are not released atsuch a rate that high pressures are generated that significantly deformthe channel shape.

FIG. 6 illustrates curves of the decomposition rate versus time for purePNB samples decomposed at both a constant temperature of about 425° C.(isothermal decomposition) and various heating rates (dynamicdecomposition), respectively. In each case, there is a peak in thedecomposition rate. The width of the peak corresponds to the transitionperiod during the conversion of sacrificial polymer to gaseous products.Higher heating rates or higher temperature isothermal decompositionsresult in a sharp peak in the decomposition rate profile. This impliesthat the majority of the decomposition process occurs over a short timeinterval, thus resulting in a sudden and large release of the gaseousdecomposition products. It was therefore expected that controlling thedecomposition rate at a constant low level using controlled heatingprofiles could eliminate this phenomena, and thus prevent channeldistortion during decomposition. It was decided to test this theory bycomparing the effect of various decomposition procedures on the finalresulting microchannel shapes and sizes.

Based on equation (6), the temperature versus time heating profilesrequired to achieve decomposition rates of 1, 2, and 3% per minute werecalculated and are illustrated in FIG. 7. The figure illustrates that,at a constant decomposition rate, the decomposition temperature duringmost of decomposition time should be set to a relatively lowtemperature, with a slight ramp rate. However as the decomposition nearscompletion, higher temperatures can be used which helps obtain completedecomposition of the polymer within a reasonable time.

Representative temperature profiles that closely approximate the smoothtemperature versus time curves produced via equation (6) were used toperform the decompositions. FIG. 8 illustrates the temperature versustime curve calculated using equation (6) and the corresponding simplemimic heating profile that was tested in the Lindberg decompositionfurnaces for device fabrication. FIG. 9 illustrates TGA results for thesimple mimic heating program that was designed to achieve a 1%/minutedecomposition rate. The DTG curve demonstrates that the decompositionrate does indeed fluctuate closely around the desired 1%/minute levelwithout extreme variations. Thus, the sharp peak in the decompositionrate shown in FIG. 6 can be avoided by using more intelligent heatingprofiles (a non-linear heating profile as a function of time). When thissame mimic heating profile is used in processing encapsulated polymersamples, no distortion in the encapsulated channels was observed butelectron microscopy revealed that small amounts of polymer residue wereleft in the channel structures. Two different modifications to the mimicheating profile were tested in an attempt to remove this residualpolymer. In the first case, a final hold at 455° C. for one hour wasused in an attempt to remove the residual polymer. This high temperaturehold did indeed reduce the residual remaining polymer substantially asobserved in SEM cross sections, but some remaining residue was left evenafter the one hour hold. A second method that involved doubling theintermediate holds shown in FIG. 8 was also tested. This effectivelyreduced the average decomposition rate even further, to somewhereapproaching the 0.5%/minute level. In this case, it was observed that nodistortion of the channel profile occurred during the decomposition andessentially no polymer residue was found in the microchannel afterdecomposition. This suggests that there may be additional byproductsformed during the decomposition if the process is ramped too quickly.This results in a residue that can be difficult to remove, even withhigh temperature processing. Longer holds at lower temperatures can beused to both slow the decomposition rate (and thus reduce patternprofile distortion) and to eliminate residual polymer in the finalchannel structures.

Microchannels encapsulated with polyimide and SiO₂: Microchannels havebeen made following the scheme in FIG. 3A through 3F. In the processing,about 3.5 to 4.0 μm thick PNB/PI film (4 wt % initiator in PNB) was castusing a spin speed of 2400 rpm and softbake condition of 110° C./60seconds. The film was exposed to UV light using a chrome on quartz maskwith dose of 450 mJ/cm² and post-exposure baked at 120° C. for 30minutes in an oven. After post-exposure baking, the film wasspray-developed using xylene to produce the desired channel patterns.There was no noticeable residue remaining after development in thepatterned areas, but direct overcoating of the encapsulant material onthe as-developed features resulted in poor adhesion to the substrate. Infact, small bubbles were observed in the overcoat materials in the areaswhere the sacrificial polymer was presumably developed cleanly away fromthe substrate. Therefore, it is possible that some small amount ofpolymer residue remains after development that prevents good adhesion ofthe overcoat to the substrate.

In order to avoid this phenomenon, a residue removal treatment wasemployed by dry-etching in an oxygen plasma using an RIE before thechannel patterns are encapsulated. After residue removal using theplasma, samples were then encapsulated using either polyimide or SiO₂.Polyimides are good materials for encapsulation because they displayhigh glass transition temperatures and thermal stability, low dielectricconstant, modulus, moisture adsorption and stress. Here, HD MicrosystemsPI 2734 polyimide, was used to overcoat some of the channel structures.In these cases, the PI 2734 was spin-coated on the top of the channelpatterns at a speed of 2300 rpm for 30 sec, and cured at 350° C. for 1hr under N₂. The thickness of the polyimide layer under these conditionsis approximately 4.5 μm. In addition, some channel structures wereencapsulated using SiO₂. In these cases, a 2-μm thick encapsulationlayer of SiO₂ was deposited using the PECVD recipe described earlier.

The decomposition of the encapsulated polymer patterns was performed atvarious decomposition rates to investigate the effect of the rate on thechannel structure. FIG. 10A through 10B illustrate SEM images of thechannel encapsulated with polyimide and decomposed at different ratesusing different heating profiles. The results indicate that thedecomposition rate does indeed affect the channel structuresignificantly. At low decomposition rates (1 or 2%/minute), the channelstructures produced maintain the size and shape of the original PNBsacrificial polymer pattern. However, at relatively high decompositionrates (3%/min) or when a high constant temperature decomposition processis used, the microchannels are distorted into dome- or arc-shapedprofiles. It is also obvious that this distortion problem becomes a moreimportant issue for microchannels as their lateral size increases.Channels with larger widths clearly deformed more than channels ofsmaller dimensions. SEM images of channels encapsulated with SiO₂ areshown in FIGS. 11A through 11F. It was observed that the extent ofchannel deformation appears to be higher in the SiO₂ overcoatedstructures as compared to the polyimide overcoated channels at the samenominal channel feature sizes and polymer decomposition rates. Thislarger deformation in the SiO₂ overcoated samples could be due to bothdifferences in the mechanical properties of the two overcoat materialsand differences in the diffusion rate of the decomposition productsthrough the overcoat materials.

Microchannels with tapered cross-section structure: In order tofabricate the tapered microchannel structures, the concept describedhere is to use a lithography process employing a gray-scale photomaskand a low contrast photosensitive sacrificial material. A series ofexperiments was performed to investigate the possibility of using suchan approach for producing microchannels that are shaped in a controlledmanner in all three dimensions.

Channel features were designed with an approximately linear gradient inpercent transmission across the width of the channel with varying ratiosof chrome stripes to clear, transparent area. In this particular case,the chrome stripe features were designed to be 200 nm in size and thusserved as sub-resolution features for the photosensitive sacrificialpolymers used in this work. Two masks were fabricated from these designsby electron beam lithography at ETEC Systems (Hayward, Calif.). Table 2describes the two main channel features used in this work in moredetail. Using this type of gray-scale mask allows for the photosensitivesacrificial material to be exposed to a range of doses across the widthof the channel feature using a single lithographic exposure step. Thisexposure gradient in conjunction with a low contrast resist material canbe used to produce a feature that is shaped in both the lateral andvertical directions with respect to the plane of the substrate in asingle lithographic process.

Two photosensitive materials with different contrast levels were used togenerate tapered microchannel structures with this mask. FIG. 12illustrates the contrast curves for the two photosensitive sacrificialpolymer formulations used in this work. The methods of measuringcontrast curves and calculating contrast values for these materials havebeen discussed previously in the literature. The contrast factors forthese two systems are a modest 0.51 and 0.85 for the 2 wt % (referred toas “material 1”) and 4 wt % (referred to as “material 2”) photoinitiatorrelative to dry polymer loadings, respectively.

TABLE 2 Characteristics of the gray-scale microchannel photomask FeatureI Channel Width 60 μm Zone Size: 6 μm 6 μm 6 μm . . . 6 μm 6 μm 6 μmTransparency (TP): 100% 90% 80% . . . 30% 20% 10% Feature II ChannelWidth 80 μm Zone Size: 4 μm 4 μm 4 μm . . . 4 μm 4 μm 4 μm Transparency(TP): 100% 95% 90% . . . 15% 10% 5%

Using this contrast curve data, it is possible to calculate a roughprediction of the pattern profile that will result from exposure using agray-scale mask with these photosensitive materials if the relativetransparency as a function of position on the mask is known accurately.Based on polynomial fitting, the contrast curves can be adequatelydescribed using the following functions:f ₁=0.0236[log(D)]³−0.357[log(D)]²+1.818[log(D)]−2.13  (7)f ₂=0.0352[log(D)]³−0.653[log(D)]²+2.95[log(D)]−2.92  (8)Here f_(i) is the fraction of the film thickness remaining afterexposure to a dose D and wet development for material i.

An approximate shape of the channel patterns that will be produced froma gray-scale mask can thus be predicted using Eq. 9,d(x)=f _(i)(log [D·TP(x)])·FT,  (9)where, f_(i) is the contrast function for material i, d(x) is thethickness of the film (after development) at a certain position x acrossthe channel pattern, TP(x) is the fractional transparency of the mask atthe position x across the feature, D is the nominal exposure dose used,and FT is the original thickness of the cast film. The outline of thesimulated channel pattern include the points calculated by Eq. 9, whichwere then smoothed by seven-point smoothing, Eq. 10.

$\begin{matrix}{S_{i} = \frac{Y_{1 - 3} + {2Y_{i - 2}} + {3Y_{i - 1}} + {4Y_{i}} + {3Y_{i + 1}} + {2Y_{i + 2}} + Y_{i + 3}}{16}} & (10)\end{matrix}$where S_(i) and Y_(i) are the smoothed signal and original signal forthe i^(th) point respectively.

Tapered-structure channel patterns were fabricated using the gray-scalelithographic approach using a sequence of steps similar to thoseoutlined in FIGS. 3A through 3F. First, 12-μm thick PNB/PI films werecast using a spin speed of 700 rpm and softbake condition of 110° C. for2 minutes. The films were then exposed to UV light with the gray-scalemask. The nominal exposure dose was set using the contrast curve datafor the photosensitive material to obtain a film with 80% originalthickness remaining after development under a 100% transparent feature.The doses used were 1300 mJ/cm² and 165 mJ/cm² for 2 wt % and 4 wt %initiator loadings, respectively. The films were post-exposure baked at120° C. for 30 minutes in oven. The films were spray developed usingxylene at a spin speed of 500 rpm for 30 seconds. The final shape of themicrochannel patterns was measured using profilometry.

FIGS. 13 and 14 illustrate the real Feature I type PNB patterns producedas measured by profilometry, and for comparison the predictedmicrochannel patterns (using equations 7 through 10), for the systemswith 2 wt % and 4 wt % initiator loadings. A comparison betweendifferent patterns produced by the two formulations clearly shows thatthe material with the lower contrast produces a profile that moreclosely resembles the desired smoothly tapered structure. However, itcan be seen that the simple prediction of the profile shape only roughlyapproximates the actual feature produced using this method. Upon closerinspection of the mask, it was apparent that the desired smooth gradientin transmission was not faithfully reproduced into the mask due to theextremely small feature sizes used for the constituent patterns. Thisbrings up the issue that accurate gray scale mask production for such amethod may in fact be a challenging task. In any case, with more carefulattention and accurate transfer of the design to the mask, it should bepossible to use the contrast data for a material in conjunction withequations (7) through (10) to design a gray-scale mask feature for aspecific photosensitive material that can be used to obtain any desiredpattern shape.

The tapered polymer microchannel patterns were next overcoated anddecomposed in order to test the ability to transfer the tapered profileinto the final microchannel. First, any polymer residue was removed fromthe substrate using an oxygen RIE plasma etch. The channel patterns werethen encapsulated with SiO₂ using the same conditions describedpreviously. The thermal decomposition of encapsulated channel patternswas performed under N₂ with a decomposition rate of 0.5%/minute. SEMimages of the resulting tapered microchannels are shown in FIGS. 15Athrough 15D. Due to the ability to carefully control the decompositionrate of the polymer by controlling the heating profile duringdecomposition, no deformation was observed in the channel structure.This can be seen by comparing the profiles of the original PNB patternsin FIGS. 13 and 14 with the SEM channel cross sections in FIGS. 15Athrough 15D. The widths of the channels in FIGS. 15A through 15D arenarrower than the feature sizes on the gray-scale mask due in part toslight RIE over-etching during the polymer residue removal step.Comparing FIGS. 15A through 15B with FIGS. 15C through 15D, it can beseen that a low contrast sacrificial material is desirable for thefabrication of smoothly tapered microchannel structures. The right handside of FIGS. 15A through 15C, and left hand side of FIGS. 15B through15D are non-gray scale features, for reference. As expected, the finalshape of the channel structure is determined by a combination of thegray-scale pattern on the mask, the contrast of the photosensitivematerial, and the nominal exposure dose used in printing the feature.

In order to obtain an idea of the effectiveness of fabricated channelcross sections in reducing dispersion in flow around microchannelcorners, the expected fluid transit times around a corner of the shapeshown in FIG. 13 were simulated using FLUENT as described previously.FIG. 16 illustrates the predicted transit times for flow around thiscorner using the boundary conditions and velocities used in the earlieridealized channel simulations. It is clear from this simulation thateven the crudely shaped channel fabricated for demonstration purposes inthis work would be expected to perform better than the standardrectangular cross section channel. Further, it is hoped that byoptimizing mask design and process conditions, that a more ideal shapesimilar to that shown in FIG. 5C can be achieved and used for devicefabrication.

CONCLUSIONS

The fabrication of microchannels has been demonstrated by usingphotosensitive sacrificial polymer materials. The process consists ofpatterning the sacrificial polymer via photolithography, removal ofpolymer residue using RIE, encapsulation with a dielectric medium, andthermal decomposition of encapsulated polymer channel patterns. A methodfor designing heating programs to keep the thermal decomposition ofsacrificial polymer at a constant rate was presented using the kineticmodel of polymer decomposition. Heating programs designed using thisapproach have been demonstrated to prevent sudden and high decompositionrates (e.g., those which result in drastic release of gaseousdecomposition products that distort channel features), and were alsoshown to produce microchannel patterns with well controlled shapes thatdo not exhibit any substantial deformation after the thermaldecomposition of the sacrificial polymer. Controlling the decompositionrate and slowly releasing the gaseous decomposition products allows thedecomposition products to permeate through the overcoat at a rateroughly equivalent to the decomposition rate, and thus avoids thebuild-up of high pressures in the microchannel which can lead todistortion and failure of the structure. It was also found that largerchannels have a greater tendency toward distortion. A gray-scalelithographic process has been developed and demonstrated for theproduction of microchannels with tapered cross-sections. Such taperedchannels have been shown through simulation to be able to reduce effectssuch as dispersion that are detrimental to microfluidic systemperformance.

It should be emphasized that the above-described embodiments of thisdisclosure are merely possible examples of implementations, and are setforth for a clear understanding of the principles of this disclosure.Many variations and modifications may be made to the above-describedembodiments of this disclosure without departing substantially from thespirit and principles of this disclosure. All such modifications andvariations are intended to be included herein within the scope of thisdisclosure and protected by the following claims.

What is claimed is:
 1. A polymer composition, comprising: aphotodefinable polymer comprising a sacrificial polymer and aphotoinitiator, the sacrificial polymer comprising analkenyl-substituted polynorbornene, wherein the photoinitiator isselected from, bis(2,4,6-trimethylbenzoyl)-phenylphosphineoxide,2-benzyl-2-dimethylamino-1-(4-morpholinophenyl)-butanone-1, andcombinations thereof.
 2. A polymer composition, comprising: aphotodefinable polymer comprising a sacrificial polymer and aphotoinitiator, the sacrificial polymer comprising analkenyl-substituted polynorbornene, wherein the sacrificial polymer isabout 1 to 30% by weight of the photodefinable polymer, thephotoinitiator is from about 0.5 to 5% by weight of the photodefinablepolymer, and the polymer composition further comprises a solvent,wherein the solvent is about 65% to 99% by weight of the photodefinablepolymer, and wherein the photoinitiator is selected from,bis(2,4,6-trimethylbenzoyl)-phenylphosphineoxide,2-benzyl-2-dimethylamino-1-(4-morpholinophenyl)-butanone-1, andcombinations thereof.
 3. The polymer composition of claim 2, wherein thephotoinitiator is a free radical generator.